Generalized Polyhedral DC Optimization Problems
The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is made on the situations where either the second component of the...
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| Vydáno v: | Journal of optimization theory and applications Ročník 207; číslo 1; s. 11 |
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Springer Nature B.V
01.10.2025
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| ISSN: | 0022-3239, 1573-2878 |
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| Abstract | The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is made on the situations where either the second component of the objective function is a generalized polyhedral convex function or the first component of the objective function is a generalized polyhedral convex function and the constraint set is generalized polyhedral convex. Various results on optimality conditions, the local solution set, the global solution set, and solution algorithms via duality are obtained. Useful illustrative examples are considered. |
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| AbstractList | The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is made on the situations where either the second component of the objective function is a generalized polyhedral convex function or the first component of the objective function is a generalized polyhedral convex function and the constraint set is generalized polyhedral convex. Various results on optimality conditions, the local solution set, the global solution set, and solution algorithms via duality are obtained. Useful illustrative examples are considered. |
| ArticleNumber | 11 |
| Author | Huong, Vu Thi Kim Huyen, Duong Thi Yen, Nguyen Dong |
| Author_xml | – sequence: 1 givenname: Vu Thi surname: Huong fullname: Huong, Vu Thi – sequence: 2 givenname: Duong Thi surname: Kim Huyen fullname: Kim Huyen, Duong Thi – sequence: 3 givenname: Nguyen Dong surname: Yen fullname: Yen, Nguyen Dong |
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| Cites_doi | 10.1007/s11228-009-0120-5 10.1007/s10107-018-1235-y 10.1007/0-387-28395-1 10.1007/s10898-023-01331-7 10.1007/s10898-010-9589-6 10.1080/02331934.2019.1614179 10.1515/9781400873173 10.1017/S0004972700010844 10.1007/978-1-4612-1394-9 10.1007/BF01463995 10.1007/s10898-019-00763-4 10.1007/s11425-008-0021-3 10.1007/s10898-023-01272-1 10.1007/s10957-015-0769-x 10.1007/978-3-030-94785-9_1 10.1137/S1052623494274313 10.1137/0802004 10.1080/01630563.2017.1387863 10.1007/s10957-023-02318-w 10.1007/s10957-010-9710-5 10.1007/s10898-020-00913-z |
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| SubjectTerms | Algorithms Convex analysis Convexity Linear programming Optimization Theorems Vector space Vector spaces |
| Title | Generalized Polyhedral DC Optimization Problems |
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